1. Applications of Normal Distributions

2. In this section we work with nonstandard normal distributions (the kind that are found in nature). To work with nonstandard normal distributions we simply standardize them, and use the techniques from the previous section. or We use our calculators!

4. Converting from a nonstandard to a standard normal distribution. 1.Sketch a normal curve, label the mean and the specific x values, then shade the region representing the desired probability. 2.For each relevant value x that is a boundary for the shaded region, find the equivalent z-score. 3.Use a calculator (normcdf(lower, upper)) or table to find the area in the shaded region.

5. The typical home doorway has a height of 6 ft 8 in. or 80 in. Given that heights of men are normally distributed with a mean of 69.0 in. And a standard deviation of 2.8. Find the percentage of men who can fit through a standard doorway without having to duck.

6. Birth weights in the U.S. are normally distributed with a mean of 3420 g and a standard deviation of 495 g. A hospital requires a special treatment for babies that are less than 2450 g or more than 4390 g. What is the percentage of babies who do not require special treatment. Do many babies require special treatment.

8. How high should doorways be if 95% of men will fit through without bending or bumping their head? Heights of men are normally distributed with a mean of 69.0 in. and a standard deviation of 2.8 in.

9. After considering relevant factors, a committee recommends special treatment for birth weights in the lowest 3% and the highest 1%. Find the birth weights that separate the lowest 3% and the highest 1%. Recall birth weights in the U.S. are normally distributed with a mean of 3420 g and a standard deviation of 495 g.

10. Homework!!! 6.2: 1- 41 eoo